Question

If the Classroom Building catches fire the amount of heat the structural support beams will be subjected to is N(2119, 251^2) degrees.

a) What is the probability that a random fire will subject the beam to temperatures between 2229 and 2358 degrees? Use 4 decimal places.

b) The beams are supposed to be built so that they only fail in 4% of the fires. What temperature do they need to be able to withstand? Round to the nearest temperature.

Answer 1

(A) Given that mean = 2119 and standard deviation = 251

we have x = 2229 and y = 2358

P(x<z<y)

(B) Beams are supposed to be built so that they only fail in 4% of the fires, so we have to find the z score corresponding to 96th percentile

using percentile table, we get z score = 1.751

Required Temperature = mean + z*sd

= 2119 +1.751*251

= 2558.501

= 2559 (nearest temperature)